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Entropy 2014, 16(4), 2223-2233; doi:10.3390/e16042223

An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion

1
Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China
2
Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA
*
Author to whom correspondence should be addressed.
Received: 24 January 2014 / Revised: 2 April 2014 / Accepted: 4 April 2014 / Published: 17 April 2014
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Abstract

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP). View Full-Text
Keywords: estimation; minimum error entropy; Renyi entropy; information potential estimation; minimum error entropy; Renyi entropy; information potential
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Chen, B.; Wang, G.; Zheng, N.; Principe, J.C. An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion. Entropy 2014, 16, 2223-2233.

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